United States Department of Agriculture Forest Service Southern Forest Experiment Station New Orleans, Louisiana General Technical Repi;;t SO-77 Stocking, Forest Type, and Stand Size Class-The Southern Forest nventory and Ana ysis Unit's Calculation of Three Important Sts-~rJ n~_ccrjntnrc - r--- Dennis M. May
The procedures by which the Southern Forest Inventory and Analysis unit calculates stocking from tree data collected on inventory sample plots are described in this report. Stocking is then used to ascertain two other important stand descriptors: forest type and stand size class. Inventory data for three plots from the recently completed 1989 Tennessee survey are used to illustrate the computation procedures. July 1990
Stocking, Forest Type, and Stand Size Class-The Southern Forest Inventory and Analysis Unit's Calculation of Three Important Stand Descriptors Dennis M. May INTRODUCTION The Forest Inventory and Analysis unit of the IJSDA Forest Service, Southern Forest Experiment Station conducts continuing surveys and reports on the forest resources in seven Midsouth States (Alabama, Arkansas, Louisiana, Mississippi, Oklahoma, Tennessee, and Texas). Data are collected from trees occurring on sample plots spaced across each State on a 3- by 3-mile grid. From these tree data, additional variables are generated that describe the forest stands in which the sample trees are located. The generation of three of these standdescription variables-stocking, forest type, and stand size class-is the focus of this paper. Data from the recent Tennessee survey are used to help illustrate the generation procedures. Stocking will be discussed first because it is essential to the generation of the other two standdescription variables. STOCKING Stocking, as defined by the Southern Forest Inventory and Analysis unit (SO-FIA), is a measure of the extent to which the growth potential of the site is utilized by trees or is preempted by other vegetation. It is expressed as the ratio (in percent) of actual stand density to a specified standard density at which the growth capacity of the site is fully utilized. The stocking standard currently in use has its origins in the Timber Resources for America's Future study (USDA FS 1958), in which stocking standards were developed for all major forest types in the United States. This was accomplished by reducing stand densities in normal yield tables for uncut natural stands to average densities that were based on the number of undamaged, free-to-grow, commercial tree species in previously cut stands on ownerships that were judged to be well managed. For sawtimber-sized trees, the 100- percent stocking standard was set at a-pproximately 60 percent of the stocking in normal stands. For seedlings and sapling-sized trees, the stocking standard was set to Table 1.- Original and current stocking standard for the South, by tree size Stocking standard Diameter class Original Current -- - --- - - -- - - -- - - -- - --- - Trees per acre-- - -- - - -- - - -- - - -- - - -- - <1 1,000 600 2 800 560 4 590 460 6 400 340 8 240 240 10 155 155 12 115 115 14 90 90 16 72 72 18 60 60 20 51 51 22 42 42 24 36 36 26 31 31 28 27 27 30 + 24 24 provide sufficient initial stocking to insure satisfactory timber quality and provide for timber yields from intermediate harvests. The stocking standard originally developed for the South was based on 1,000 seedlings per acre, but was later reduced to reflect a basis of 600 seedlings per acre. This reduction was applied only to trees 6 inches in diameter at breast height (d.b.h.) and smaller in order to account for changes in southern forest management since 1958 (table 1). This stocking standard is used in the derivation of each plot's relative stocking percentage. Each live tree tallied contributes a relative stocking percentage to the plot total based on its size, its corresponding specified stocking standard, and the Sampling design under which it was selected (tables 2,3,4). The SO-FLA tallies trees 5 inches in d.b.h. and larger on a cluster of 10 horizontal prism points (basal area Dennis M. May is research forester, U.S. Department of Agriculture, Forest Service, Southern Forest Experiment Station, Starkville, MS 39759. 1
Table 2.-Example plot consisting of an overstocked stand of seedling to sapling-sized loblolly pines* Relative Prism stocking point Species Crown class D.b.h. Tree class percentage Incher 1 Yellow-poplar 1.1 4.709 Loblofly pine Intemediate 1.0 Growing -stock 4.690 2 Yellow-poplar Intemediate 0.1 4.600 Dogwood Intemediate 0.1 4.600 Dogwood Intemediate 0.1 4.600 Yellow-poplar Intemediate 0.1 2.200 3 Northern red oak 0.1 4.600 Yellow-poplar 0.1 4.600 Yellow-poplar 0.1 4.600 Yellow-poplar 0.1 2.200 4 Dogwood 1.0 4.690 5 Loblolly pine 1.3 4.753 Loblolly pine 1.3 4.753 Loblolly pine 1.0 4.690 6 Loblolly pine 1.7 4.859 Loblolly pine 1.3 4.753 7 Loblolly pine 1.6 4.830 Loblolly pine 1.4 4.777 Loblolly pine 1.4 4.777 8 Loblollypine 1.4 4.777 Loblolly pine 1.1 4.709 9 Loblolly pine 0.1 4.600 Blackgum 0.1 4.600 Loblolly pine 0.1 4.600 Loblolly pine 0.1 2.200 10 Loblolly pine 0.1 4.600 Blackgum 0.1 4.600 Blackgum 0.1 4.600 Yellow-poplar 0.1 2.200 *Plot summary: Stocking (all live) 125.767 percent Stocking (growing-stock) 120.990 percent Forest typing All live stocking (%) Softwoods 54 Pines Loblolly pine Yellow-poplar Dogwood Blackgum Northern red oak Tree-size class Seedlingisapling 100
Table 3.-Exampleplot up land site * consisting of an optimally stocked stand ofpole-sized white oak on an Relative Prism stocking point Species Crown class D.b.h. Tree class percentage A3 obaes 1 Whiteoak 6.0 2 8.8 3 Post oak 4 5 Hickory 6 Black oak 7 Sourwood 8 Sourwood Black gum Black gum 9 Hickory Sourwood 10 9.3 *Plot summary: Stocking (all live) 90.657 percent Stocking (growing-stock) 75.676 percent Forest typing All live stocking (%) Hardwoods 100 71 Soumood Hickory Black oak Post oak Black gum Tree-size class Seedlingisapling Pole Sawtimber
Table 4.-Example plot consisting of an understocked stand of sawtiher-sized cottonwood on a bottomland site* Relative Stocking Point Species Crown class Bee class percent I Cottonwood Osage-orange Grovving-stock 2 Sugarberry Sugarberry 4 Cottonwood Cottonwood 5 Cottonwood Cotton wood Cot tonwood Willow 6 Cottonwood Cot tonwood 7 Cottonwood Hickory 8 Cottonwood Cottonwood Honeylocust 10 Sycamore Osage-orange Intermeaiate *Plot summary: Stocking (all live) 76.693 percent Stocking (growing-stock) 37.200 percent Forest typing All live stocking (5%) Hardwoods 100 Cottonwood 47 Osage-orange Sugarberry Sycamore Honeylocust Willow Hickory li-ee-size class Pole Sawtimber 63
factor 37.5) and tallies trees less than 5 inches in d.b.h. on ten 11275-acre circular fixed plots associated with each prism point, As a consequence, relative stocking percentages can be calculated from the following formulas: Relative stocking percentage for a prism point tree=[(37.5 square feet per acre) +- (basal area of the tally tree) + (number of points per sample plot) +(appropriate size-class stocking standard)](100). For example, relative stocking percentage for a 6- inch tally tree=[(37.5) + (0.1963) +- (10) +- (340)](100) ~ 5.6 percent. Relative stocking percentage for fixed-plot tree= [(trees per acre represented by each tally tree) +(number of fixed plots per sample plot) + (appropriate size-class stocking standard)] (100). For example, relative stocking percentage for a 4- inch tally tree= [(275) + (10) +- (460)](100) =6.0 percent. These general formulas and the stocking standards in table 1 have been used to calculate relative stocking percentages for different-sized tally trees collected under the SO-FIA sample design (table 5). Only data for the 2- and 4-inch classes are shown in table 5, but tally trees from 1.0 to 4.9 inches in d.b.h. are actually assigned relative stocking percentages by 0.10-inch classes using the following formula: (4.5865) + (0.0229) (d.b.h.)+(0.0807) (d.b.h.12. This procedure for calculating relative stocking percentages is modified in certain special circumstances. Seedlings, which are defined as trees with a d.b.h. of less than 1.0 inch, are tallied and assigned a stocking percentage only if they occur on sample points where no trees Table 5.-Relative stocking percentages assigned to tally trees in given diameter classes Diameter class Relative tree stocking Irtches Percent <1 4.6 2 5.o 4 6.0 6 5.6 8 4.5 10 4.4 12 4.2 14 3.9 16 3.8 18 3.5 20 3.4 22 3.4 24 3.3 26 3.3 28 3.3 30 + 3.2 are larger than. seedlings (table 2). Also, in the early 1970's it was determixled that smaller trees, which are assigned relative stocking percentages that are greater than those assigned to larger trees, were given disproportionate weight in the determination of forest type. This cawed same pine stan& to bc typed by the hardwood understory and not by the softwood overstory. To alleviate this problem, the stocking percentages assigned to sapling-sized trees (d.b.h. between 1'0 and 4.9 inch'es) on sample points with at least one tree whose d.b.h. is 5.0 inches or larger are discounted using the following formula, which was proposed by the Southeastern Forest Experiment Station: Discounted stocking percentage= (0.1957) (d.b.h.12. The discounting procedure was applied in table 3, sample points 7 and 8. Finally, points having no live tally trees are assigned a percentage that refers not to the relative stocking of trees but to the proportion of the plot preempted from tree growth by other vegetation or other conditions. With a 10-point sample cluster, this percentage is 10. This percentage is not used in the calculation of relative plot stocking. In the next step, relative tree stocking at each point is summed to yield point occupancy. Point occupancy is allowed to accumulate to 16 percent per point and to a maximum of 160 percent per plot. As the current 100- percent stocking standard was set at approximately 60 percent of normal stocking, the 160-percent maximum can be regarded as the proportional equivalent of stocking levels represented by normal yield tables. Actually, the maximum percentage should be 167 percent, but has been reduced down to the "160 percent plus7' category shown in the Forest Survey Handbook (USDA FS 1972). Allowing each point to contribute no more than a given maximum to point occupancies ensures that no one point or group of points has a disproportionate weight in determining stocking, forest type, or stand size class, This is especially important when the sample plot consists of a cluster of 10 prism points that cover approximately 1 acre. In the summation of point occupancy, preference is given to the most open-grown and largest trees. This is accomplished by sorting the tally trees by crown class and d.b.h. (tables 2, 3, 4). Thlly trees less than 5 inches in d.b.h., which are not assigned to crown classes in the field, are subsequently assigned to the intermediate crown class. The stocking percentage of the tally tree that causes the point occupancy to exceed 16.0 percent is reduced until point occupancy equals 16.0 percent (table 2, sample points 2, 3, 9, 10). The relative stocking percentages for trees dropped from the point occupancy accumulation are set at zero (table 3, sample point 4). The relative stocking percentages of the trees that contribute to point occupancies are summed to determine relative stocking for each plot. Relative plot stocking is commonly based only on tallies and measurements of i
Table 6,---General species gvoupings used in the detemirtation of forest type Timber types Managements types General forest types Detailed forest types Softwood Pine White pine-hemlock Jack pine Red pine White pine White pine-hemlock Hemlock White-red-jack pine Longleaf-slash pine Loneleaf-slash pine Longleaf pine Slash pine Loblolly-shortleaf pine Loblolly-shortleaf pine Loblolly pine Shortleaf pine Virginia pine Sand pine Eastern redcedar Pond pine Spruce pine Pitch pine Table-mountain pine Other softwood Spruce-fir Balsam fir Black spruce Red spruce Northern white-cedar Tamarack White spruce Mixed softwood/hardwood Mixed pinelhardwood Oak-pine White pine-northern red oak- white ash Eastern redcedar-hardwood Longleaf pine-scrub oak Shortleaf pine-oak Virginia pine-southern red oak Loblolly pine-hardwood Slash pine-hardwood Other oak-pine Hardwood Upland hardwood Bottomland hardwood Oak-hickory Post-black-bear oak Chestnut oak White-red oak-hickory Northern red oak Yellow-poplar-white oak-northern red oak Southern scrub oak Sweetgum-yellow-poplar Mixed hardwoods Maple-beech-birch Sugar maple-beech-birch Aspen-birch Aspen Birch Oak-gum-cypress Swamp chestnut-cherrybark oak Sweetgum-Nuttal oak-willow oak Sugarberry-American elm-green ash Overcup oak-water hickory Atlantic white-cedar Cypress-tupelo Sweetbay-swamp tupelo-red maple Elm-ash-cottonwood Black ash-american elm-red maple River birch-sycamore Cottonwood Willow Sycamore-pecan-American elm Nontyped
growing-stock trees, but can also be based on tallies and measurements of live trees (growing-stock trees plus rough and rotten cull trees). The relative plot stocking is then used to place the plot in one of several broad stocking classes: Relative plot stocking Stocking class 16.7 percent Nonstocked 16.7 to 60 percent Understocked (table 4) 60 to 100 percent Optimally stocked (table 3) >100 percent Overstocked (table 2) FOREST TYPE Determinations of forest type are not made in the field. Instead, they are made on the basis of computations that involve the use of tally-tree data. This assures consistency in forest type classifications over time, which in turn make it possible to assess trends accurately. In general, a forest type takes its name from the species or species group that forms the plurality of relative plot stocking. In the actual typing process, forest types are named by determining the proportions of relative plot stocking in increasingly detailed species groupings, which are shown in table 6. First it is determined whether softwood species (excluding cypress) comprise at least half of the plot stocking. If so, then classification of the plot as a pine or other softwood type depends on whether pine species (including red cedar) comprise the majority of the softwood stocking. The specific species of pine or other softwood that forms the plurality of the pine or other softwood plot's stocking then determines the general and detailed forest type classifications. For example, in table 2 softwoods comprise 54 percent of relative plot stocking, pines comprise 100 percent of softwood stocking, and loblolly pines comprise all of the pine stocking, resulting in a loblolly-shortleaf general forest type and loblolly detailed forest type classifications. If softwoods fail to comprise the majority of relative plot stocking, but pines still comprise 25 to 49 percent, then a mixed forest type will be assigned by determining which pine species has the largest proportion of stocking. If pine stocking is less than 25 percent of relative plot stocking, then a hardwood type is assigned. Whether a plot is classified as an upland or bottomland hardwood type depends entirely on the physiographic class assigned by the forester in the field. When a plot is located on a upland physiographic site, an upland hardwood type is assigned; when a plot is located on a bottomland physiographic site, a bottomland hardwood type is assigned. Beyond this point, the general forest type and detailed forest type are named for the hardwood species or species grouping that forms the plurality of stocking (tables 4,5). Forested plots lacking live tally trees, recent clearcuts for example, are classified as nontyped. STAND SIZE CLASS Stand size class is also generated from the relative stocking percentages assigned to live tally trees. For plots containing enough live tally trees to have a relative plot stocking of at least 16.7 percent, each live tally tree is assigned to one of the following tree-size classes based on it%d.b.h.: 1. Seedlinglsapling (trees less than 5 inches in d.b.h.), 2. Pole (softwood trees from 5.0 to 8.9 inches in d.b.h. and hardwood trees from 5.0 to 10.9 inches in d.b.h.), and 3. Sawtimber (trees greater than pole-size). Relative stocking percentages for all trees in each size class are summed, and the proportion of total plot stocking represented by the size class is calculated. If trees in the seedlinglsapling size class comprise at least half of the plot stocking then the plot is classed as seedlinglsapling (table 2). If not, then the plot's size class will depend on whether the pole-sized trees or sawtimber-sized trees comprise the greater proportion of the plot's stocking (tables 3, 4). Plots with relative stocking percentages below 16.7 are classified as nonstocked. CONCLUSIONS A clear understanding of the procedures used to calculate stocking, forest type, and stand size class is essential to correct understanding, interpretation, and use of SO-FIA forest resource data. The SO-FIA procedures for computation of these stand descriptors from treelevel inventory data were developed to reflect real-world conditions. However, the assumptions upon which the techniques are based will not hold true in every situation. Fortunately, these occasional misrepresentations of existing conditions are compensated for by the consistency these computational techniques lend to assessments of long-term trends. LITEWTURE CITED U.S. Department of Agriculture, Forest Service. 1958. Timber resources for America's future. Forest Resour. Rep. No. 14. Washington, DC: U.S. Department of Agriculture. 713 p. U.S. Department of Agriculture, Forest Service. 1972. Forest Survey Handbook. In: Forest Service Handbook 1809.11. Amendment 6. Section 21.5. Washington, DG: U.S. Department of Agriculture.
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I May, Dennis M. 1990. Stocking, forest type, and stand size class-the Southern Forest Inventory and Analysis unit's calculation of three important stand descriptors. Gen. Tech, Rep. SO-77. New Orleans, LA: U.S. Department of Agriculture, Forest Service, Southern Forest Ekperiment Station. 7 p. Data from three forest inventory plots collected in the 1989 survey of Tennessee are used to demonstrate how the Southern Forest Inventory and Analysis unit calculates plot stocking, forest type, and stand size class from forest inventory sample tree data. Keywords: Forest inventory, sample plot, stocking class, stocking percentage, stocking standard.